Nuprl Lemma : es-class-def_wf
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A,B:Type]. ∀[X:EClass(B)]. ∀[R:E ⟶ A ⟶ ℙ]. ∀[F:e:E ⟶ {a:A| R[e;a]} ⟶ B].
(∀a,e such that R[e;a]
e∈X with value F[e;a] ∈ ℙ)
Proof
Definitions occuring in Statement :
es-class-def: es-class-def,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
es-class-def: es-class-def,
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top,
so_apply: x[s],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
es-E-interface: E(X)
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,B:Type]. \mforall{}[X:EClass(B)]. \mforall{}[R:E {}\mrightarrow{} A {}\mrightarrow{} \mBbbP{}]. \mforall{}[F:e:E
{}\mrightarrow{} \{a:A| R[e;a]\}
{}\mrightarrow{} B].
(\mforall{}a,e such that R[e;a]
e\mmember{}X with value F[e;a] \mmember{} \mBbbP{})
Date html generated:
2016_05_17-AM-06_42_47
Last ObjectModification:
2015_12_29-AM-00_25_56
Theory : event-ordering
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